Find the 18th term of the sequence 5, 8, 11, 14, 17...

Assume that the population of the world in 2017 was 7.6 billion and is growing at the rate of 1.12% a year. a) Set up a recurren

Dmitry_Shevchenko [17]

Answer:

a) $= 1.0112 a_{n-1}$

b) $= 7.6 . 1.0112^n$

c) $a_{33} = 10.97 billion$

Step-by-step explanation:

Given data:

Population in 2017 was 7.6 billion

r = 1.12%

a) population after n year 2017

It is given each year population rise at a rate of 1.12% Thus we have

$a_n = a_{n-1} + 1.12%.a_{n-1}$

$= a_{n-1} + 0.0112 a_{n-1}$

$= 1.0112 a_{n-1}$

b) $a_{n} = 1.0112 a_{n-1}$

$a_{n} = 1.0112 a_{n-1} = 1.011 ^1 a_{n-1}$

$a_{n} = 1.0112 a_{n-2} = 1.011 ^2 a_{n-2}$

$a_{n} = 1.0112 a_{n-3} = 1.011 ^3 a_{n-3}$

....

$= 1.0112^n a_{n-n}$

$= 1.0112^n a_{0}$

$= 7.6 . 1.0112^n$

c) for n = 33 year ( 2050- 2017 = 33 year)

$a_{33} = 7.6 \times 1.0112^33$

$a_{33} = 10.97 billion$

6 0

3 years ago

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Derive the equation of the parabola with a focus at (−5, −5) and a directrix of y = 7.

asambeis [7]

Answer:

Answer: The equation of the parabola is (x+5)^2=-24(y-1)(x+5)

2

=−24(y−1) .

3 0

2 years ago

Write down in terms of n, an expression for the nth term

Nimfa-mama [501]

Answer:

$a_{n}$ = - 7n - 1

Step-by-step explanation:

There is a common difference between consecutive terms , that is

- 15 - (- 8) = - 22 - (- 15) = - 29 - (- 22) = - 36 - (- 29) = - 7

This indicates the sequence is arithmetic with nth term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 8 and d = - 7 , then

$a_{n}$ = - 8 - 7(n - 1) = - 8 - 7n + 7 = - 7n - 1

7 0

2 years ago

Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorat

mr_godi [17]

Answer:

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

Step-by-step explanation:

We formulate our null and alternative hypotheses as

H0 u≤ 6 ug Ha : u > 6 ug

The significance level ∝ = 0.05

The test statistic used is

t = X` - u / s/ √n

which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.

The critical region t > t (0.05,11) = 1.796

We compute the t value from the data

Xi Xi²

8.92 79.5664

6.99 48.8601

5.54 30.6916

5.73 32.8329

6.38 40.7044

5.51 30.3601

6.45 41.6025

7.50 56.25

8.48 71.9104

5.56 30.9136

6.90 47.61

6.46 41.7316

80.42 553.0336

Now x` = ∑x/ n = 80.42/12 = 6.70

S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)

= 1/11 (553.034-538.948) = 1.2805

s= 1.1316

Putting the values in the test statistics

t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12

= 2.1698

The critical region t > t (0.05,11) = 1.796

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

6 0

3 years ago

The ponce de leon lighthouse in St.Augustine, Florida, is the second tallest brick tower in the United States.It was built in 18

vovikov84 [41]

Using a right triangle formed by boat with base and top of lighthouse.Note: 15 minutes = 0.25 degreesLet d be distance the boat is from shore.tan(90−13.25)=d/175
d=175∗tan(76.75)=743.2

6 0

3 years ago

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